一类相对转动非线性动力学系统周期解的唯一性与精确周期解  

Precise periodic solutions and uniqueness of periodic solutions of some relative rotation nonlinear dynamic system

作　　者：王坤[1,2] 关新平[2] 乔杰敏[1] 

机构地区：[1]燕山大学理学院,秦皇岛066004 [2]燕山大学电气工程学院,秦皇岛066004

出　　处：《物理学报》2010年第6期3648-3653,共6页Acta Physica Sinica

基　　金：国家杰出青年科学基金(批准号:60525303)资助的课题~~

摘　　要：研究了一类具有线性刚度、非线性阻尼力和强迫周期力项的相对转动非线性动力学系统周期解的唯一性和精确周期解.讨论了一类自治系统极限环的唯一性与稳定性.应用定性分析方法,给出了一类相对转动非线性动力学系统具有唯一周期解的必要条件,并在一定条件下得到了系统的一类精确周期解.The precise periodic solution and uniqueness of periodic solutions of some relative rotation nonlinear dynamical system possessing linear rigidity and nonlinear damping force and forcing periodic force is investigated. Firstly,the stability and uniqueness of limit cycles of a kind of autonomous nonlinear dynamical system are discussed. Secondly,the necessary condition of uniqueness of periodic solutions of the system is presented by using qualitative analysis method. The precise periodic solution of the system is obtained under certain conditions.

关 键 词：相对转动 非线性动力系统 极限环 周期解 

分 类 号：O302[理学—力学]